Representing geometric objects using constraint description graphs

Abstract

The paper demonstrates how geometrical constraints can be applied to add a new level of abstraction to description of geometrical objects. Special attention is given to the interactive insertion of constraints. To support incremental design each inserted constraint has to be solved as soon as possible. Because of this requirement a local propagation of known states is used for constraint solving. It is supported by a biconnected constraint description graph structure. The benefits of this structure are insensibility to the order of inserted constraints and ability of replacing constraints with their inverse couples. To override the ambiguities at constraint solving the approximal values of geometrical elements which are inserted through a sketch are used. From the biconnected constraint description graph an acyclic constraint description graph is generated easily. It is suitable for the generation of instances of generic objects.